It is widely recognized that atrial fibrillation (AF) predisposes patients to embolic stroke and systemic emboli. Although oral anticoagulant therapy has been suggested to decrease the incidence of embolic events, its benefits have not been proven and its attendent risks of hemorrhage prevent its application without confirmed benefits. The purpose of this study is to evaluate the benefits and risks of oral anticoagulant therapy in reducing embolic stroke and systemic emboli in patients with AF, without rheumatic heart disease. The benefits and risks of anticoagulation will be evaluated by a randomized, controlled trial assigning patients to treatment (anticoagulation) and no treatment groups. If treatment is beneficial, the annual incidence of embolic events should decrease from 5% in the control group to less than 1% in the treatment group. The incidence of hemorrhagic complications of the treatment and control groups will be quantitated to evaluate the risks of therapy.